However, since ES relies on observations exceeding the VaR, it is clear that assessment of ES forecasts cannot be independent of the predicted VaR values.
This, together with the fact that ES is not elicitable, motivates the introduction of a scoring function for jointly evaluating VaR and ES forecasts. Based on the characterization of consistent scoring functions introduced by [1]} and [2]}, several scoring rules have been proposed in the literature for the univariate setting (see, e.g., [3]}, [4]} and [5]}).
